Limits
1s, 512 MB
·
Custom Checker
Construct a square matrix $a$ of size $n×n$ satisfying the following conditions,
- Each row of the matrix is a permutation of size
$n$ - Each column of the matrix is a permutation of size
$n$ - The matrix is symmetric, that means
$a[i][j] = a[j][i]$for all possible$i,j$$(1≤i,j≤n)$ - The matrix satisfies
$a[i][i] = i$for all$i$$(1≤i≤n)$
If it is possible to build such a matrix, print the matrix otherwise print $-1$.
Input
First line of input consists of a single integer $T$, the number of test cases $(1 ≤ T ≤ 5)$
Each test case consists of one line. First and only line of the test case contains $n$, the dimension of the matrix. $(1 ≤ n ≤ 1000)$.
Output
Print the matrix if possible, otherwise print $-1$. If there are multiple possible answers, anyone would be acceptable.
Sample
| Input | Output |
|---|---|
2 2 3 | -1 1 3 2 3 2 1 2 1 3 |
We call a sequence of integers $A$ permutation if every integer from 1 to |A| appears exactly once in the sequence, where $|A|$ denotes the length of the sequence.
